Finite Group Databasebeta

← #34197945

Subgroups — #34197945

Order 20224.

426 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23767717C211yesmaximal, characteristic
2#23761741C211yesmaximal, characteristic
3#23761349C214yesmaximal, complemented
4C79×#1459C211yesmaximal, characteristic
5C22×C4⋊Dic79C411yescharacteristic
6#19098620—21no—
7#19098502—21no—
8#19098499—21no—
9#19098461—21no—
10#19098443C412yes—
11#19098435C2212yes—
12#19098423—21no—
13#19098423C411yescharacteristic
14#19098287—21no—
15#19098287C2212yes—
16C2×C4×D4×C79C2211yescharacteristic
17C2×C22⋊C8×C79—21no—
18#324×C79—21no—
19#323×C79C2212yes—
20C23×Dic79C2×C412yes—
21C2×C4⋊Dic79—21no—
22C2×C4⋊Dic79—21no—
23C2×C4⋊Dic79—21no—
24C2×C4⋊Dic79—41no—
25C2×C4⋊Dic79—41no—
26C2×Dic79⋊C4—22no—
27C2×C22⋊Dic79—22no—
28C2×C22⋊Dic79C2×C412yes—
29C4⋊(C79⋊C8)—41no—
30C22⋊(C79⋊C8)—22no—
31#14579072—41no—
32C79⋊#95—21no—
33C79⋊#95—22no—
34C79⋊#95—22no—
35C22×D4×C79C2×C411yescharacteristic
36C23×C4×C79C2×C411yescharacteristic
37C23×C4×C79D411yescharacteristic
38C22×C8×C79—41no—
39C4×D4×C79—41no—
40C4×D4×C79—41no—
41C2×C4⋊C4×C79D411yescharacteristic
42C2×C22⋊C4×C79D411yescharacteristic
43C2×C22⋊C4×C79C2311yescharacteristic
44C2×C42×C79D411yescharacteristic
45C22⋊C8×C79—22no—
46C22⋊C8×C79—41no—
47C22×Dic79—22no—
48C22×Dic79—22no—
49C22×Dic79—42no—
50C22×Dic79—82no—
51C2×C79⋊C8—42no—
52C4⋊Dic79—42no—
53C4⋊Dic79—42no—
54C4⋊Dic79—41no—
55C4⋊Dic79—41no—
56Dic79⋊C4—82no—
57C22⋊Dic79—24no—
58C22⋊Dic79—82no—
59C24×C79C22⋊C411yescharacteristic
60C24×C79C22×C411yescharacteristic
61C2×D4×C79—22no—
62C2×D4×C79—22no—
63C2×D4×C79—41no—
64C22×C4×C79—21no—
65C22×C4×C79—21no—
66C22×C4×C79—21no—
67C22×C4×C79—21no—
68C22×C4×C79—42no—
69C22×C4×C79—42no—
70C22×C4×C79C22⋊C411yescharacteristic
71C22×C4×C79C22⋊C411yescharacteristic
72C22×C4×C79C22⋊C411yescharacteristic
73C22×C4×C79C2×D411yescharacteristic
74C22×C4×C79C2×D411yescharacteristic
75C2×C8×C79—42no—
76C2×C8×C79—82no—
77C4⋊C4×C79—41no—
78C22⋊C4×C79—41no—
79C22⋊C4×C79—41no—
80C42×C79—21no—
81C42×C79—21no—
82C23×C79—21no—
83C23×C79—21no—
84C23×C79—21no—
85C23×C79—21no—
86C23×C79—41no—
87C23×C79—41no—
88C23×C79—41no—
89C23×C79—41no—
90C23×C79#10112yes—
91C23×C79C2×C22⋊C411yescharacteristic
92C23×C79#13112yes—
93D4×C79—44no—
94C2×C4×C79—22no—
95C2×C4×C79—21no—
96C2×C4×C79—21no—
97C2×C4×C79—21no—
98C2×C4×C79—21no—
99C2×C4×C79—21no—
100C2×C4×C79—21no—
101C2×C4×C79—42no—
102C2×C4×C79—42no—
103C2×C4×C79—42no—
104C2×C4×C79—41no—
105C2×C4×C79—41no—
106C2×C4×C79—41no—
107C2×C4×C79—81no—
108C2×C4×C79#9911yescharacteristic
109C2×C4×C79#9911yescharacteristic
110C2×Dic79—42no—
111C2×Dic79—42no—
112C2×Dic79—42no—
113C2×Dic79—42no—
114C2×Dic79—42no—
115C2×Dic79—42no—
116C2×Dic79—84no—
117C8×C79—82no—
118C79⋊C8—82no—
119C22×C79—21no—
120C22×C79—21no—
121C22×C79—22no—
122C22×C79—22no—
123C22×C79—42no—
124C22×C79—42no—
125C22×C79—42no—
126C22×C79—41no—
127C22×C79—41no—
128C22×C79—41no—
129C22×C79—41no—
130C22×C79—81no—
131C22×C79#40811yescharacteristic
132C22×C79C2×#9911yescharacteristic
133C22×C79C2×#10111yescharacteristic
134C4×C79—21no—
135C4×C79—41no—
136C4×C79—41no—
137C4×C79—41no—
138C4×C79—41no—
139C4×C79#35212yes—
140Dic79—82no—
141Dic79—82no—
142#11576—791nomaximal, Sylow
143C2×C79—21no—
144C2×C79—21no—
145C2×C79—42no—
146C2×C79—42no—
147C2×C79#147211yescharacteristic
148C2×C79C2×#35211yescharacteristic
149C2×C79#212211yescharacteristic
150#2487—791no—
151#1466—791no—
152#1459D7911yescharacteristic
153#1326—794no—
154C79#1157611yescharacteristic, complemented, Sylow
155C2×C4×D4C2×D7911yescharacteristic
156C22×C4⋊C4—791no—
157#432—1581no—
158C2×C22⋊C8—21no—
159#400—1581no—
160#399—1581no—
161#389—1581no—
162#386—792no—
163#385—792no—
164#380—791no—
165#380—1581no—
166#324—21no—
167#323—792no—
168#323—1581no—
169#323C2×D7912yes—
170C22×D4C4×D7911yescharacteristic
171C23×C4—792no—
172C23×C4C4×D7911yescharacteristic
173C23×C4C22⋊D7911yescharacteristic
174C22×C8—41no—
175C4×D4—41no—
176C4×D4—41no—
177C2×C4⋊C4—3161no—
178C2×C4⋊C4—3161no—
179C2×C4⋊C4—1581no—
180C2×C4⋊C4—1581no—
181C2×C4⋊C4—1581no—
182C2×C4⋊C4—1582no—
183C2×C4⋊C4C22⋊D7911yescharacteristic
184C2×C22⋊C4—792no—
185C2×C22⋊C4—1582no—
186C2×C22⋊C4D31611yescharacteristic
187C2×C22⋊C4C22×D7911yescharacteristic
188C2×C42D31611yescharacteristic
189C4⋊C8—3161no—
190C22⋊C8—22no—
191C22⋊C8—41no—
192C22⋊C8—1582no—
193#97—3161no—
194#95—1581no—
195#95—1582no—
196#95—1582no—
197C24(C2×D79)⋊C411yescharacteristic
198C24C2×C4×D7911yescharacteristic
199C2×D4—22no—
200C2×D4—22no—
201C2×D4—41no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—3162no—
209C22×C4—6322no—
210C22×C4—1582no—
211C22×C4—1582no—
212C22×C4(C2×D79)⋊C411yescharacteristic
213C22×C4(C2×D79)⋊C411yescharacteristic
214C22×C4(C2×D79)⋊C411yescharacteristic
215C22×C4C2×C22⋊D7911yescharacteristic
216C22×C4C2×D31611yescharacteristic
217C2×C8—42no—
218C2×C8—82no—
219C2×C8—3162no—
220C4⋊C4—41no—
221C4⋊C4—3162no—
222C4⋊C4—3162no—
223C4⋊C4—3161no—
224C4⋊C4—3161no—
225C4⋊C4—6322no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—6322no—
229C22⋊C4—1584no—
230C42—21no—
231C42—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23#1457907912yes—
241C23C2×(C2×D79)⋊C411yescharacteristic
242C23#1457916712yes—
243D4—44no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—81no—
258C2×C4—3162no—
259C2×C4—3162no—
260C2×C4—3162no—
261C2×C4—3162no—
262C2×C4—3162no—
263C2×C4—3162no—
264C2×C4—6324no—
265C2×C4#1457907511yescharacteristic
266C2×C4#1457907511yescharacteristic
267C8—82no—
268C8—6322no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—81no—
281C22#1909852911yescharacteristic
282C22C2×#1457907511yescharacteristic
283C22C2×#1457907911yescharacteristic
284C4—21no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—6322no—
290C4—6322no—
291C4#1909835212yes—
292C2—21no—
293C2—21no—
294C2—42no—
295C2—42no—
296C2#2376176311yescharacteristic
297C2C2×#1909835211yescharacteristic
298C2#2376505111yescharacteristic
subgroupG/H
centerC22C2×#14579075
commutatorC24×C79C22×C4
FrattiniC2×C22⋊C4C22×D79
FittingC79×#1459C2
socleC22×C79C2×#99
prime radicalC22×D4×C79C2×C4
cosocleC2×C22⋊C4×C79C23
hypercenter#1459D79
hypocenterC79#11576
LCSG ▷ C24×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #23761349C2semidirect
154. C79#11576semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237677172
#237617412
#237613492
C79×#14592
#1157679